1. **State the problem:** Expand and simplify the expression $8.(2x - 9)(3x + 4)$. 2. **Recall the distributive property:** To expand $(a+b)(c+d)$, multiply each term in the first parentheses by each term in the second: $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the distributive property to $(2x - 9)(3x + 4)$:** $$ (2x)(3x) + (2x)(4) + (-9)(3x) + (-9)(4) = 6x^2 + 8x - 27x - 36 $$ 4. **Combine like terms:** $$ 6x^2 + (8x - 27x) - 36 = 6x^2 - 19x - 36 $$ 5. **Multiply the entire expression by 8:** $$ 8 \times (6x^2 - 19x - 36) = 48x^2 - 152x - 288 $$ 6. **Final answer:** $$ \boxed{48x^2 - 152x - 288} $$